How do you find the value of a given the points (2,-5), (a,7) with a distance of 15?

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Answer 1 · 2017-06-11T22:50:36

See a solution process below:

The formula for calculating the distance between two points is:

$d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2)$

Substituting the values from the problem for the points and the distance and then solving for $a$ gives:

$15 = sqrt((color(red)(a) - color(blue)(2))^2 + (color(red)(7) - color(blue)(-5))^2)$

$15 = sqrt((color(red)(a) - color(blue)(2))^2 + (color(red)(7) + color(blue)(5))^2)$

$15 = sqrt((color(red)(a) - color(blue)(2))^2 + 12^2)$

$15 = sqrt((color(red)(a) - color(blue)(2))^2 + 144)$

$15^2 = (sqrt((color(red)(a) - color(blue)(2))^2 + 144))^2$

$225 = (color(red)(a) - color(blue)(2))^2 + 144$

$225 = a^2 - 4a + 4 + 144$

$225 = a^2 - 4a + 148$

$225 - color(red)(225) = a^2 - 4a + 148 - color(red)(225)$

$0 = a^2 - 4a - 77$

$0 = (a - 11)(a + 7)$

Solution 1)

$a - 11 = 0$

$a - 11 + color(11) = 0 + color(11)$

$a - 0 = 11$

$a = 11$

Solution 1)

$a + 7 = 0$

$a + 7 - color(7) = 0 - color(7)$

$a + 0 = -7$

$a = -7$

$a$ can be either $-7$ or $11$